The Research of Epidemics Spreading on Complex Networks

The study on complexity science, modeling and behavior of complex systems, structures functions and dynamical processes on complex networks have become a new research branch of science research which emerged at the end of last century. Especially in the field of complex networks, more and more domestic and foreign scientists have been attracted. In recent years, the discoveries of complex networks have attracted a lot of interest which has been applied extensively in many fields, such as graph theory, statistical physics, Computer networks, ecology, sociology and Economics. Many behaviors, such as the spread of the virus in Computer networks, the prevalence of infectious diseases in the crowd, diffusion of canard in society and so on, can be viewed as the communication on the networks which is subjected to a certain law. It is a great importance to study the virus spreading on complex networks and explore the diffusing mechanism as well as preventive measures. In this paper, we have a pilot study on the behavior of virus spreading on complex networks. The content is as follows:Firstly, by considering the individual variation effects on the epidemic spreading inhomogeneous networks, we study critical conditions of different scenarios. We conclude that the threshold value of spreading velocity is determined by the network topology, which has no connection with the individual characteristics through theoretical analysis and numerical simulation. We extend the critical condition of classical SIS model by introducing average spreading velocity of individuals in networks. Only if the average spreading velocity lager than the threshold value of spreading velocity can the epidemic spreads, otherwise, it dies out. So we conclude that, even if there exist some very powerfully infectious individuals, an epidemic will not be possible if the proportion of these infectious individuals is below a certain value.In the next place, we study the effects of initial infected proportion on the epidemic spreading in complex networks. Through theoretical analysis, we conclude that with a settled effective spreading velocity, the time which epidemic spreading needs to reach a stable state and the infected density of the network which is in the stable state are both linearly depending on the initial infected ratio. The bigger the initial infected ratio, the shorter time it takes to reach a stable state. The larger the degree index of scale-free networks, the faster the spreading velocity and the greater the spreading intensity of epidemics.Thirdly, we introduce the feedback mechanism into homogeneous networks, and study the epidemic spreading behaviors based on classical SIS model. Then we take WS small-world network model for example, and the results of simulations show that the value of density p in stable state decreases as the value of modulating parameterÎ±increases. Therefore, the feedback mechanism is a very effective mechanism to control epidemic spreading.Finally, we present a conclusion for this thesis and some prospects for future work in this field.

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